{
  "abstract": "In this paper we study the motivic Chabauty--Kim method, which aims to determine the set of $S$-integral points of $\\mathbb{P}^1\\smallsetminus \\{0,1,\\infty\\}$, over cyclotomic fields. We focus on the case $K=\\mathbb{Q}(ζ_8)$ and $S=\\left\\{(1-ζ_8)\\right\\}$, where we obtain explicit polylogarithmic Kim functions up to depth $4$ and verify Kim's Conjecture for several primes. We also observe and explain that the Chabauty--Kim locus for the polylogarithmic quotient contains, in addition to the $S$-integral points, certain exceptional points arising from roots of unity in $\\mathbb{Q}_p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01128",
  "author_total": 3,
  "authors": [
    {
      "name": "Minhyong Kim"
    },
    {
      "name": "Xiang Li"
    },
    {
      "name": "Martin Lüdtke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ydwpw2mf98ap.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01128",
  "fulltext_url": null,
  "id": "1ydwpw2mf98ap",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01128",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7206188337",
  "pdf_url": "https://arxiv.org/pdf/2609.01128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ydwpw2mf98ap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields",
  "title_text": "Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/1ydwpw2mf98ap",
  "venue": "arXiv",
  "versions": []
}